The other thing you will find is most lab supplies with a constant current mode will have a very small output capacitor, for my 30V / 10A one, it only uses 47uF, but its so well built that i only see 35mV of ripple at full load (it is a switch mode based bench supply)
This is so the output voltage can fall very quickly when the current load changes to something greater than the limit.
In reality if you are intending to run something like an LED, you would set the current limit, turn the voltage limit to 0, connect the device and wind back up, as that output capacitor will always mean there will be some kind of spike when coming from a higher voltage, or at the very least set the voltage close to what you expect.
And i will warn you one thing that will bite you in the backside building your own, like i did mine, stability with non resistive loads, e.g. how does your supply react to being connected to car battery, or a large drill motor, or something that pulls spikes of current at a frequency,